Double-Hopf Bifurcation in an Oscillator With External Forcing and Time-Delayed Feedback Control
Keyword(s):
In this paper an oscillator with time delayed velocity feedback controls is studied in detail. The particular attention is focused on internal double-Hopf bifurcation with an external exciting force. Linear analysis is used to find the critical conditions under which a double-Hopf bifurcation occurs. Then center manifold theory is applied to obtain an ODE system described on a four-dimensional center manifold. Further, the technique of multiple-time scales is employed to find the approximate solutions of periodic and quasi-periodic motions. Finally, numerical simulation results are presented to verify the analytical predictions. Also, for some certain parameter values, numerical results show chaotic attractors.
2006 ◽
Vol 16
(12)
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pp. 3523-3537
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2013 ◽
Vol 23
(01)
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pp. 1350014
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2009 ◽
Vol 19
(11)
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pp. 3733-3751
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2007 ◽
Vol 10
(04)
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pp. 423-448
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